Both of these share the same, difficult-to-photograph imprint found on the other two examples which have turned up:

“Doran Deliance Providence RI Pat Pend.” The fact that none have surfaced with a “Patented” imprint is a good indication that these were extinct by the time the Dorans’ patent was granted in 1925. So now we know they also came in ringtops. Also, note that terrific clip on the other example? That explains the slits in the barrel of the first example of these I found: